Experimental Research on the Use of a Selected Multi-Criteria Method for the Cutting of Titanium Alloy with an Abrasive Water Jet
Abstract
:1. Introduction
2. Materials and Method
2.1. Materials
2.2. The VIKOR Method
- m—number of options, n—number of initial conditions.
- ri,j is the normalized element of the decision matrix.
- fi,j—normalized matrix element,
- xi,j—element of the relative decision matrix.
- wi—attribute weight.
- ν—impact factor. The VIKOR coefficient can take any value between 0 and 1.
2.3. Experimental Setup and Equipment
- -
- The diameter of the water nozzle: 0.3 mm,
- -
- The diameter of the water-abrasive nozzle: 0.76 mm,
- -
- The distance of the nozzle from material: 4 mm.
3. Results and Discussion
- -
- Water nozzle diameter: 0.3 mm,
- -
- Diameter of the water-abrasive nozzle focusing tube: 0.76 mm,
- -
- Nozzle-to-material distance: 4 mm.
- -
- Condition 1. Advantage is accepted: Q(A(2) − Q(A(1) ≥ 1/(m−1) where A(1) is the alternative highest ranked, and A(2) is the next alternative after Q and m is the number of alternatives.
- -
- Condition 2. Stability is accepted. This means that the alternative A(1) must also meet the requirement of the highest grade of S and/or R.
- -
- Solution 1. When Condition 1 is not met then the value of A(m) is determined by Q(A(m)) − Q(A(1)) < 1/(m−1) for the largest value of m (these alternatives are close to each other).
- -
- Solution 2. When Condition 2 is not met, the compromise is A(1) and A(2).
- -
- Solution 3. When Condition 1 and Condition 2 are not satisfied, the compromise solution is the smallest value of Q.
- -
- Pressure is the most important factor and the smallest dispersion can be observed at 400 MPa;
- -
- The abrasive flow rate is a parameter that slightly affects the surface roughness;
- -
- The optimum traverse speed for minimum surface roughness.
- -
- Pressure = 400 MPa;
- -
- Abrasive flow rate = 450 g/min;
- -
- Traverse speed = 150 mm/min.
- -
- Determination of points: ideal and anti-ideal;
- -
- Calculation of the weighted average distance from the ideal point Si and the maximum weighted distance from the ideal point Ri for each object;
- -
- Determination of the comprehensive Qi index for each variant followed by the construction of three rankings based on the calculated values according to the principle: the lower the value of the index, the higher the position in the ranking;
- -
- Selecting the first variant from the Qi ranking and comparing it with the variant immediately after it in this ranking; two conditions are checked at this stage—acceptable advantage and acceptable stability of the decision—on the basis of the information obtained. It is decided which variant or variants are compromise solutions.
4. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Element | Contents [%] |
---|---|
Carbon | 0.08 max |
Nitrogen | 0.05 max |
Oxygen | 0.20 max |
Hydrogen | 0.0125 max |
Vanadium | 3.50–4.50 |
Aluminum | 5.50–6.75 |
Iron | 0.25 max |
Feature | Unit | Values | |
---|---|---|---|
Fe3Al2(SiO4)3+ Mg3Al2(SiO4)3+ Ca3Al2(SiO4)3 | % | 92.0–98.0 | |
Chemical composition | Fe3O4+ NaCa2(Mg, Fe, Al)3(SiAl)8O22(OH)2+ KAlSi3O8+ (Ca, K, Na, Fe, Mg, Mn, Li, Al)2-3 (OH, F)2(Si, Al4O10) | % | 4.0–8.0 |
CaCO3 | % | <0.2 | |
SiO2 | % | <0.5 | |
ZrSiO4 | % | <0.2 | |
Melting temperature | °C | 1315 | |
Density | kg/m3 | 3900–4100 |
No. | Input Parameters | Output Parameters | |||
---|---|---|---|---|---|
Beneficial | Non-Beneficial | ||||
Abrasive Flow Rate [g/min] | Pressure [MPa] | Traverse Speed [mm/min] | Cutting Depth [mm] | Roughness Sq [mm] | |
1 | 250 | 360 | 50 | 8.47 | 4.64 |
2 | 250 | 380 | 150 | 5.16 | 4.56 |
3 | 250 | 400 | 250 | 3.61 | 4.99 |
4 | 350 | 360 | 150 | 5.05 | 5.35 |
5 | 350 | 380 | 250 | 3.59 | 7.07 |
6 | 350 | 400 | 50 | 9.64 | 4.08 |
7 | 450 | 360 | 250 | 3.48 | 4.86 |
8 | 450 | 380 | 50 | 8.93 | 4.82 |
9 | 450 | 400 | 150 | 5.35 | 4.33 |
Criterium | Cutting Depth [mm] | Roughness Sq [μm] |
---|---|---|
entropy | 0.537320329 | 0.608208812 |
dispersion | 0.462679671 | 0.391791188 |
weight | 0.54 | 0.46 |
Beneficial | Non-Beneficial | |
---|---|---|
Cutting Depth | Roughness Sq | |
[mm] | [μm] | |
alternative1 | 8.47 | 4.64 |
alternative2 | 5.16 | 4.56 |
alternative3 | 3.61 | 4.99 |
alternative4 | 5.05 | 5.35 |
alternative5 | 3.59 | 7.07 |
alternative6 | 9.64 | 4.08 |
alternative7 | 3.48 | 4.86 |
alternative8 | 8.93 | 4.82 |
alternative9 | 5.35 | 4.33 |
Beneficial | Non-Beneficial | |
---|---|---|
Cutting Depth [mm] | Roughness Sq [μm] | |
alternative1 | 0.444439 | 0.3072390 |
alternative2 | 0.270756 | 0.3019417 |
alternative3 | 0.189425 | 0.3304143 |
alternative4 | 0.264985 | 0.3542518 |
alternative5 | 0.188375 | 0.4681421 |
alternative6 | 0.505832 | 0.2701584 |
alternative7 | 0.182603 | 0.3218063 |
alternative8 | 0.468577 | 0.3191577 |
alternative9 | 0.280726 | 0.2867122 |
R | S | Q | |
---|---|---|---|
alternative1 | 0.425849 | 0.811450 | 0.809727 |
alternative2 | 0.439869 | 0.569691 | 0.701410 |
alternative3 | 0.364513 | 0.374559 | 0.529915 |
alternative4 | 0.301424 | 0.422746 | 0.493022 |
alternative5 | 0.008500 | 0.008500 | 0 |
alternative6 | 0.523988 | 1 | 1 |
alternative7 | 0.387295 | 0.387295 | 0.558436 |
alternative8 | 0.421147 | 0.815452 | 0.807185 |
alternative9 | 0.480176 | 0.624680 | 0.768236 |
R Value | Rank in R | S Value | Rank in S | Q Value | Rank in Q | |
---|---|---|---|---|---|---|
alternative1 | 0.425849 | 6 | 0.811450 | 7 | 0.809727 | 8 |
alternative2 | 0.439869 | 7 | 0.569691 | 5 | 0.701410 | 5 |
alternative3 | 0.364513 | 3 | 0.374559 | 2 | 0.529915 | 3 |
alternative4 | 0.301424 | 2 | 0.422746 | 4 | 0.493022 | 2 |
alternative5 | 0.008500 | 1 | 0.008500 | 1 | 0 | 1 |
alternative6 | 0.523988 | 9 | 1 | 9 | 1 | 9 |
alternative7 | 0.387295 | 4 | 0.387295 | 3 | 0.558436 | 4 |
alternative8 | 0.421147 | 5 | 0.815452 | 8 | 0.807185 | 7 |
alternative9 | 0.480176 | 8 | 0.624680 | 6 | 0.768236 | 6 |
Condition 1 | Acceptance |
Condition 2 | Acceptance |
Selected solution | Solution 3 |
No. | Input Parameters | Output Parameters | |||
---|---|---|---|---|---|
Beneficial | Non-Beneficial | ||||
Abrasive Flow Rate [g/min] | Pressure [MPa] | Traverse Speed [mm/min] | Cutting Depth [mm] | Roughness Sq [mm] | |
5 | 350 | 380 | 250 | 3.59 | 7.07 |
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Radomska-Zalas, A. Experimental Research on the Use of a Selected Multi-Criteria Method for the Cutting of Titanium Alloy with an Abrasive Water Jet. Materials 2023, 16, 5405. https://doi.org/10.3390/ma16155405
Radomska-Zalas A. Experimental Research on the Use of a Selected Multi-Criteria Method for the Cutting of Titanium Alloy with an Abrasive Water Jet. Materials. 2023; 16(15):5405. https://doi.org/10.3390/ma16155405
Chicago/Turabian StyleRadomska-Zalas, Aleksandra. 2023. "Experimental Research on the Use of a Selected Multi-Criteria Method for the Cutting of Titanium Alloy with an Abrasive Water Jet" Materials 16, no. 15: 5405. https://doi.org/10.3390/ma16155405
APA StyleRadomska-Zalas, A. (2023). Experimental Research on the Use of a Selected Multi-Criteria Method for the Cutting of Titanium Alloy with an Abrasive Water Jet. Materials, 16(15), 5405. https://doi.org/10.3390/ma16155405